# Bayesian Optimization for Dynamic Pricing and Learning

arXiv: https://arxiv.org/abs/2510.12447 · HTML: https://mlsanity.com/paper/2510.12447/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 66 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 28 of 28)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Noisy Networks for Exploration](https://mlsanity.com/paper/1706.10295/) (2017)
- [(More) Efficient Reinforcement Learning via Posterior Sampling](https://mlsanity.com/paper/1306.0940/) (2013)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Parameter Space Noise for Exploration](https://mlsanity.com/paper/1706.01905/) (2017)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Linear Contextual Bandits with Knapsacks](https://mlsanity.com/paper/1507.06738/) (2015)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [An efficient algorithm for contextual bandits with knapsacks, and an extension to concave objectives](https://mlsanity.com/paper/1506.03374/) (2015)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Reward-Free Model-Based Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2110.06394/) (2021)
- [Contrasting Exploration in Parameter and Action Space: A Zeroth-Order Optimization Perspective](https://mlsanity.com/paper/1901.11503/) (2019)
- [Volumetric Spanners: an Efficient Exploration Basis for Learning](https://mlsanity.com/paper/1312.6214/) (2013)
- [Unscented Bayesian Optimization for Safe Robot Grasping](https://mlsanity.com/paper/1603.02038/) (2016)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)
- [Efficient Exploration of Gradient Space for Online Learning to Rank](https://mlsanity.com/paper/1805.07317/) (2018)
- [Scalable Gaussian-process regression and variable selection using Vecchia approximations](https://mlsanity.com/paper/2202.12981/) (2022)
- [Parallel Gaussian Process Regression with Low-Rank Covariance Matrix Approximations](https://mlsanity.com/paper/1305.5826/) (2013)
- [Parallel Gaussian Process Regression for Big Data: Low-Rank Representation Meets Markov Approximation](https://mlsanity.com/paper/1411.4510/) (2014)
- [Reinforcement Learning algorithms for regret minimization in structured Markov Decision Processes](https://mlsanity.com/paper/1608.04929/) (2016)
- [Bayesian Optimization for Function Compositions with Applications to Dynamic Pricing](https://mlsanity.com/paper/2303.11954/) (2023)
- [Practical First-Order Bayesian Optimization Algorithms](https://mlsanity.com/paper/2306.10815/) (2023)
- [Revenue Maximization in Service Systems with Heterogeneous Customers](https://mlsanity.com/paper/1605.07107/) (2016)
- [Static Pricing: Universal Guarantees for Reusable Resources](https://mlsanity.com/paper/1905.00731/) (2019)

## Abstract (arXiv)

Dynamic pricing is the practice of adjusting the selling price of a product to maximize a firm's revenue by responding to market demand. The literature typically distinguishes between two settings: infinite inventory, where the firm has unlimited stock and time to sell, and finite inventory, where both inventory and selling horizon are limited. In both cases, the central challenge lies in the fact that the demand function -- how sales respond to price -- is unknown and must be learned from data. Traditional approaches often assume a specific parametric form for the demand function, enabling the use of reinforcement learning (RL) to identify near-optimal pricing strategies. However, such assumptions may not hold in real-world scenarios, limiting the applicability of these methods. In this work, we propose a Gaussian Process (GP) based nonparametric approach to dynamic pricing that avoids restrictive modeling assumptions. We treat the demand function as a black-box function of the price and develop pricing algorithms based on Bayesian Optimization (BO) -- a sample-efficient method for optimizing unknown functions. We present BO-based algorithms tailored for both infinite and finite inventory settings and provide regret guarantees for both regimes, thereby quantifying the learning efficiency of our methods. Through extensive experiments, we demonstrate that our BO-based methods outperform several state-of-the-art RL algorithms in terms of revenue, while requiring fewer assumptions and offering greater robustness. This highlights Bayesian Optimization as a powerful and practical tool for dynamic pricing in complex, uncertain environments.